139
GAS LAWS
- were derived by experiment long before kinetic theory, but agree with the kinetic picture!
True at constant temperature
Boyle's Law:
True at constant temperature
Charles's Law:
True at constant pressure, and
using ABSOLUTE temperature
True at constant pressure, and
using ABSOLUTE temperature
140
Combined gas law:
Must use ABSOLUTE
temperature units!
Must use ABSOLUTE
temperature units!
Avogadro's law:
- a mole of any gas at the same conditions has the same volume.
Standard
Temperature
and
Pressure
11.1"
11.1"
11.1"
= 22.4 L
141
Ideal gas law:
... but this constant actually depends on the amount
of gas!
The ideal gas constant.
... combining these together ...
P = pressure
V = volume
T = ABSOLUTE temperature
R = ideal gas constant
n = number of moles of gas molecules
142
CHEMICAL CALCULATIONS WITH THE GAS LAWS
Given 25.0 g of sodium bicarbonate and sufficient sulfuric acid, what volume of carbon
dioxide gas would be produced at 25.0 C and 0.950 atm pressure?
1 - Convert 25.0 g of sodium bicarbonate to moles using formula weight.
2 - Convert moles sodium bicarbonate to moles carbon dioxide using chemical equation.
Notice this is very similar
3 - Convert moles carbon dioxide to volume using ideal gas equation
to chapter 3 calculations!
REMEMBER: The units for P, V, and
T MUST MATCH the units in R.
143
What volume would the gas in the last example problem have at STP?
STP: "Standard Temperature and Pressure" (0 C and 1 atm)
Since the number of moles of gas is fixed, use combined gas law.
An alternate solution: Use the number of moles of gas we calculated previously, then plug
into the ideal gas equation.
144
At 300 C, ammonium nitrate violently decomposes to produce nitrogen gas, oxygen gas,
and water vapor. What is the total volume of gas that would be produced at 1.00 atm by
the decomposition of 15.0 grams of ammonium nitrate?
A shortcut: Since the volume doesn't depend on the IDENTITY of the gas molecules, we'll
calculate the TOTAL NUMBER OF MOLES of gas and use that in the ideal gas equation.
1 - Convert 15.0 grams of ammonium nitrate to moles using formula weight.
2 - Convert moles ammonium nitrate to TOTAL MOLES OF GAS using chemical equation
3 - Convert TOTAL MOLES OF GAS to volume using ideal gas equation.
Try at home, Calculate the PRESSURE if this same amount of ammonium nitrate were
decomposed in a 30 mL fixed-volume container.
145
REAL GASES
- The empirical gas laws (including the ideal gas equation) do not always apply.
- The gas laws don't apply in situations where the assumptions made by kinetic
theory are not valid.
- When would it be FALSE that the space between gas molecules is much
larger than the molecules themselves?
- at high pressure, molecules would be much closer together!
- When would it be FALSE that attractive and repulsive forces would be
negligible?
- at high pressure, attractions and repulsions should be stronger!
- at low temperature, attractions and repulsions have a more
significant affect on the paths of molecules
slow (low T)
fast (high T)
-The gas laws are highly inaccurate near the point where a gas changes to
liquid!
- In general, the lower the pressure and the higher the temperature, the more
IDEAL a gas behaves.
van der Waals equation
146
- an attempt to modify PV = nRT to account for several facts.
- gas molecules actually have SIZE (they take up space)
- attractive and repulsive forces
Ideal gas equation
van der Waals
equation
attempts to account for molecular size
attempts to account for attractive / repulsive forces
* "a" and "b" are experimentally determined parameters
that are different for each gas.
tiny, no special attractive forces
small, but strong attractions
between moleculres
larger, and strong attractions between
molecules
147
2500 L of chlorine gas at 25.0 C and 1.00 atm are used to make hydrochloric acid. How many
kilograms of hydrochloric acid could be produced if all the chlorine reacts?
1- Convert 2500 L of chlorine gas to moles using the ideal gas equation.
2 - Convert moles of chlorine gas to moles hydorchloric acid using chemical equation.
3 - Convert moles HCl to mass using formula weight.
Remember to keep track of
what substance we're
currently calculating
148
Calculate the mass of 22650 L of oxygen gas at 25.0 C and 1.18 atm pressure.
1 - Convert the volume of oxygen to moles using ideal gas equation.
2 - Convert moles oxygen to mass using formula weight.
Volume of a 10'x10'x8'
room
149
If 48.90 mL of hydrochloric acid solution react with sodium carbonate to produce 125.0 mL
of carbon dioxide gas at 0.950 atm and 290.2 K. What is the molar concentration of the acid?
What is M?
1 - Convert 125.0 mL of carbon dioxide gas to moles using ideal gas equation.
2 - Convert moles carbon dioxide to moles HCl using chemical equation
3 - Calculate molarity of HCl from moles HCl and volume HCl.